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CHOICE OF THE OPTIMAL DISTRIBUTION OF CROP AREAS IN THE AGRO-INDUSTRIAL SECTOR BASED ON THE MARKOVITZ MODEL
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D.A. Hercekovich ' , Candidate of Technical Sciences, Associate Professor O.L. Podlinyaev , Doctor of Psychology, Professor international College of Economics and Linguistics Irkutsk State University (Russia, Irkutsk)
S.N. Larin3, Candidate of Technical Sciences, Leading Researcher Central Economics and Mathematics Institute RAS (Russia, Moscow)
DOI: 10.24411/2411-0450-2020-10702
Abstract. In the last few years the agro-industrial sector of the Russian economics shows stable growth rates. It was immeasurably contributed by the implementation by Russia of the food import ban in reply to sanction restrictions of leading Western countries and of its allies. With that the agro-industrial complex itself undergoes pivotal structural transformations, oriented to the increase of the efficiency of its functioning. Mentioned circumstances predetermined the high topicality of this research subject.
The article represents the terms of reference for the best distribution of crop areas. To solve such a task was used the Markovitz model, based on basic provisions of the portfolio analysis. The task has been solved while takig into account the agriculture specifics in the territory of Russia. Were provided results of the analysis of the effective distribution of crop areas for the growing of agricultural crops on the example of one and several sites. With that at the federal level as entities of the Russian Federation - area and/or region. At the regional level this term will be relevant at the distribution of crop areas at the level of districts. Within a district the comparative analysis of the efficiency of the use of crop areas is expedient for categories of agricultural enterprises.
Keywords: agro-industrial complex, crop area distribution, optimal choice, portfolio investment theory, Markowitz model.
As we know, the difference of kinds of soils, climatic conditions and other factors considerably influences the different fitness of certain districts and land plots for certain agricultural crops. The role of the right selection of the crops plan cannot be overstated. So, for example, the barley better grows in Northern areas, while the wheat grows better in Southern areas. Anyway, nowadays there are cases of the use of administrative management methods. These methods do not take into account in what region such or such culture is growing in what frames its yield can be obtained. In this juncture we have to solve the optimization task for the purpose of the effective redistribution of existing cultivation areas in order to obtain the higher yield of grown agricultural crops. The implementation of this approach creates the background for the in-
crease of the gross yield of the agricultural production in species and in value terms, without recourse to the increase of cultivation areas. The approach to its solution will be offered in the article hereunder.
Literature review
To the modern research in the field of the mathematical support to the financial management are referred developments of innovative strategies of the development and instrumental means of the improvement of efficiency of the decision making at the management of investments in certain security assets. This trend comprises technical analysis methods, substantiated in works of Charles LeBeau and of David Lucas [1], Alexander Elder [2, 3] and many other academic economists. This trend comprises also methods of the applied regression analysis as well as of time sequence analy-
sis, which have been highlighted in works of such scientists as Norman Draper and Harry Smith [4], John Seber [5], John Box and Henry Jenkins [6], Irving Fisher etc. The other trend refers to the portfolio investment theory. There are best known works of Harry Markovitz [7], William Sharp, Gordon Alexander, Jeffrey Bailey [8], James Tobin [9], Zvi Bodie and Robert Merton [10] etc. This research can been based on the analysis of the cumulative effect from investments in different investment instruments, provided its cross-effect. In spite of the variety of works for the modernization of investment mechanisms at financial markets, the problem of the coordination of different approaches and of the creation of the comprehensive investment system have not been duly developed.
Methods
The process of formation of innovative development strategies, as well as the making of investment decisions, is contingent on the variety of many alternative options of the distribution of cultivated areas and of the referred risk. Investors, ready to invest funds in the growing of agricultural crops, encounter the problem of the adequate and objective risk evaluation, as well as of prospective for the value realization for investments. The later circumstance is directly related to the yield growth of different agricultural crops. Above mentioned factors have predetermined the need for the following modernization of portfolio investment methods. The analysis of investment qualities of the whole stockpile of investment portfolio strategies of economical entities of the agro-industrial complex should become the most important trend. On the basis of evaluation results is carried out the substantiated selection for the most optional distribution of positive areas and of related strategic development trends in application to activities of a certain economic entity.
Methods of the performed research is based on the theory of portfolio investment and on the Markovitz model, adapted for terms of functioning of the Russian agro-industrial complex.
Results and Discussion
In the provided position the studied task should be referred to the class of mathemati-
cal problems. Let's consider the process of such task decision in terms of its complexity.
A. Optimization of the distribution of one land cultivation areas.
This is the task of the classic linear programming with the cultivated area of q (ha), on which it plans to grow three cereal crops: A, B and C. After the harvesting it is assumed to sell the harvest of the grain A, collected from 1 ha for c1 rubles, (so from the general sale of this culture yield the farmer will get c xq x rubles), B grain - forc2 rubles and C - for c3 rubles. It is necessary to determine, how much of ha of land a farmer should provide for each of above mentioned cultures in order to obtain the maximal profit? Let's introduce following indices: L - target function, q1, q2, q3 - accordingly, cultivated lands, which, accordingly, are to be provided for A, B and C cultures. Then the target function should be recorded as follows:
(1)
where qi > 0, for i = 1, 2, 3 (nonnegative variables);
(the sum of qi shares is equal to the whole site area).
Under the conditions of problem resources restrictions can be applied to following resources: crop of cultures, its treatment in the period of the grain maturing, processing, sorting, its treatment in the grain maturing period, as well as the period for the cleaning sorting, processing, transportation etc. Provided the following extension of terms of reference up to the real one let's consider the most current restriction:
a i < u ¡qj < b i, for i = 1, 2, 3.
where - site needs in a relevant culture;
b i - its liquidity.
The essence of the last restriction is as follows: the task of the optimization of the distribution of cultivated lands for the studied site is determined not only by its options (soil capabilities, climatic terms etc.), but also while taking into account needs of the population, residing in this territory, as well as industrial needs of this district. The above men-
tioned is referred to the interpretation of left parts of inequations. As to right parts of inequations, it is designed for the provision for sales of the grown agricultural production after it has been collected.
B. Optimization of the distribution of cultivated areas and sites with relevant cultivated lands of n sites with relevant cultivated areas
q1, q2, ..., qn.
The academician of the AS USSR, Nobel laureate L.V. Kantorovich was the first one, who generally formulated the mathematical problem of the distribution of cultivated areas [11]. Here such term as "site" is used in the more broad sense, namely: it can be cultivated areas of any countries (if assumed, that all countries of our planet (or some part of it) «have agreed» on the common search of more rational ways of use of global land resources). At the federal level we will assume as sites entities of the Russian Federation - area and/or region etc. At the regional level it will be most appropriate to divide areas into districts. At district scales the comparative analysis of the efficiency of cultivated areas can be performed by categories of entities etc. Then it is assumes to carry out the quantitative assay of the rationality of placement of m cultures at these areas. Let's assume that at i site the expected crop yield of the k culture is ui;k (centners from the hectare). And its price is ck (rubles per centner). It is obvious, that such detailing is not excessive for Russia due to the very high differentiation of the quality of tillable lands, weather conditions, seeds' technologies, harvest maintenance and collection, traditions etc.
It is necessary to determine how much hectares from each site of q1, q2, ., qn it is necessary to occupy for each culture among above mentioned once - m in order to obtain the maximal profit. Let's mark as hi;k the area (ha) of the i site, occupied for the planting of the k culture. Then the amount £ k= 1 h ik = qi is equal to the total area of the i site (it is assumed that hi;k > 0), and the amount of is equal to the planting area under the k culture from the total m number.
Then the target function looks as follows:
L= £ £= iCkZ H iu i k h k( m ax) (2)
where
As in the previous topic there can be resource restrictions, which are not considered within frames of the article hereunder, i.e. existing restrictions for needs and liquidity for each culture among studied ones seem more timely. Let's highlight that £ ■= 1u i kh k is the expected final harvest for each culture in the whole considered territory (for which the optimization is being performed, where i = 1, 2, ..., m). Then the relevant restriction can be recorded in the form of double inequation:
ak < £ F= iu i k h i k < b k (3)
The sample of the practical implementation of the Markovitz model with the "Solution search" suspension MS EXCEL is contained in the work [12]. Most practicing investors consider that the distinctive feature of the Markovitz model is the comparative difference of its direct implementation, though on the other side the approach allows to make play different scenarios, which not only contribute to the synthesis of effective working investment strategies, but also provide for the additional information, enriching the investor with the fuller appreciation of the studied task.
Conclusion
On the basis of results, obtained in the course of the performed research, following opinions should be formed.
1. Under the influence of structural transformations in the agro-industrial complex it became necessary to solve such problem as the best distribution of cultivated lands.
2. For this purpose it was offered to use Markovitz models on the basis of the portfolio analysis.
3. Obtained results allow to assume that with this model can be obtained effective distributions of cultivated lands for the growing of agricultural crops.
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ВЫБОР ОПТИМАЛЬНОГО РАСПРЕДЕЛЕНИЯ ПОСЕВНЫХ ПЛОЩАДЕЙ В
АГРОПРОМЫШЛЕННОМ СЕКТОРЕ НА ОСНОВЕ МОДЕЛИ МАРКОВИЦА
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Д.А. Герцекович ' , канд. техн. наук, доцент О.Л. Подлиняев2, д-р психол. наук, профессор 1Международный институт экономики и лингвистики 2Иркутского государственного университета (Россия, г. Иркутск)
С.Н. Ларин3, канд. техн. наук, ведущий научный сотрудник 3Центральный экономико-математический институт РАН (Россия, г. Москва)
Аннотация. Агропромышленный сектор российской экономики в последние годы показывает устойчивые темпы роста. Этому во многом способствовало введение Россией продовольственного эмбарго в ответ на санкционные ограничения ведущих стран Запада и их союзников. Вместе с тем, в самом агропромышленном комплексе происходят кардинальные структурные преобразования, направленные на повышение эффективности его функционирования. Указанные обстоятельства предопределили высокую актуальность тематики данного исследования.
В статье представлена постановка задачи наилучшего распределения посевных площадей. Для ее решения была использована модели Марковица, в основу которой положены базовые положения портфельного анализа. Решение задачи проведено с учетом специфики земледелия на территории России. Приведены результаты анализа эффективного распределения посевных площадей для выращивания сельскохозяйственных культур на примере одного и нескольких участков. При этом на федеральном уровне под участками будем подразумевать субъекты Российской Федерации - края и/или области. На региональном уровне этот термин будет уместным при распределения посевных площадей на уровне районов. В масштабе района сравнительный анализ эффективности использования посевных площадей целесообразно проводить по категориям сельскохозяйственных предприятий.
Ключевые слова: агропромышленный комплекс, распределения посевных площадей, оптимальный выбор, теория портфельных инвестиций, модель Марковица.
